Investigations of MgB 2 and Fe-based superconductors in recent years have revealed many unusual effects of multiband superconductivity but manifestations of anisotropic multiband effects in the critical current density J c have not been addressed experimentally, mostly because of the difficulties to measure J c along the c-axis. To investigate the effect of very different intrinsic anisotropies of σ and π electron bands in MgB 2 on current transport, we grew epitaxial films with tilted c-axis (θ ~ 19.5 o ), which enabled us to measure the components of J c both along the ab-plane and the c-axis using magneto-optical and transport techniques. These measurements were combined with scanning and transmission electron microscopy, which revealed terraced steps on the surface of the c-axis tilted films. The measured field and temperature dependencies of the anisotropic J c (H) show that J c,L parallel to the terraced steps is higher than J c,T perpendicular to the terraced steps, and J c of thinner films (50 nm) obtained from transport experiments at 0.1 T reaches ∼10% of the depairing current density J d in the ab plane, while magneto-optical imaging revealed much higher J c at lower fields. To analyze the experimental data we developed a model of anisotropic vortex pinning which accounts for the observed behavior of J c in the c-axis tilted films and suggests that the apparent anisotropy of J c is affected by current pairbreaking effects in the weaker π band. Our results indicate that the out-of-plane current transport mediated by the π band could set the ultimate limit of J c in MgB 2 polycrystals.2